1 Import Dataset

## Parsed with column specification:
## cols(
##   instant = col_double(),
##   dteday = col_date(format = ""),
##   season = col_double(),
##   yr = col_double(),
##   mnth = col_double(),
##   holiday = col_double(),
##   weekday = col_double(),
##   workingday = col_double(),
##   weathersit = col_double(),
##   temp = col_double(),
##   atemp = col_double(),
##   hum = col_double(),
##   windspeed = col_double(),
##   casual = col_double(),
##   registered = col_double(),
##   cnt = col_double()
## )
## # A tibble: 6 x 16
##   instant dteday     season    yr  mnth holiday weekday workingday weathersit
##     <dbl> <date>      <dbl> <dbl> <dbl>   <dbl>   <dbl>      <dbl>      <dbl>
## 1       1 2011-01-01      1     0     1       0       6          0          2
## 2       2 2011-01-02      1     0     1       0       0          0          2
## 3       3 2011-01-03      1     0     1       0       1          1          1
## 4       4 2011-01-04      1     0     1       0       2          1          1
## 5       5 2011-01-05      1     0     1       0       3          1          1
## 6       6 2011-01-06      1     0     1       0       4          1          1
## # … with 7 more variables: temp <dbl>, atemp <dbl>, hum <dbl>, windspeed <dbl>,
## #   casual <dbl>, registered <dbl>, cnt <dbl>
## # A tibble: 6 x 16
##   instant dteday     season    yr  mnth holiday weekday workingday weathersit
##     <dbl> <date>      <dbl> <dbl> <dbl>   <dbl>   <dbl>      <dbl>      <dbl>
## 1     726 2012-12-26      1     1    12       0       3          1          3
## 2     727 2012-12-27      1     1    12       0       4          1          2
## 3     728 2012-12-28      1     1    12       0       5          1          2
## 4     729 2012-12-29      1     1    12       0       6          0          2
## 5     730 2012-12-30      1     1    12       0       0          0          1
## 6     731 2012-12-31      1     1    12       0       1          1          2
## # … with 7 more variables: temp <dbl>, atemp <dbl>, hum <dbl>, windspeed <dbl>,
## #   casual <dbl>, registered <dbl>, cnt <dbl>
##     instant          dteday               season            yr        
##  Min.   :  1.0   Min.   :2011-01-01   Min.   :1.000   Min.   :0.0000  
##  1st Qu.:183.5   1st Qu.:2011-07-02   1st Qu.:2.000   1st Qu.:0.0000  
##  Median :366.0   Median :2012-01-01   Median :3.000   Median :1.0000  
##  Mean   :366.0   Mean   :2012-01-01   Mean   :2.497   Mean   :0.5007  
##  3rd Qu.:548.5   3rd Qu.:2012-07-01   3rd Qu.:3.000   3rd Qu.:1.0000  
##  Max.   :731.0   Max.   :2012-12-31   Max.   :4.000   Max.   :1.0000  
##       mnth          holiday           weekday        workingday   
##  Min.   : 1.00   Min.   :0.00000   Min.   :0.000   Min.   :0.000  
##  1st Qu.: 4.00   1st Qu.:0.00000   1st Qu.:1.000   1st Qu.:0.000  
##  Median : 7.00   Median :0.00000   Median :3.000   Median :1.000  
##  Mean   : 6.52   Mean   :0.02873   Mean   :2.997   Mean   :0.684  
##  3rd Qu.:10.00   3rd Qu.:0.00000   3rd Qu.:5.000   3rd Qu.:1.000  
##  Max.   :12.00   Max.   :1.00000   Max.   :6.000   Max.   :1.000  
##    weathersit         temp             atemp              hum        
##  Min.   :1.000   Min.   :0.05913   Min.   :0.07907   Min.   :0.0000  
##  1st Qu.:1.000   1st Qu.:0.33708   1st Qu.:0.33784   1st Qu.:0.5200  
##  Median :1.000   Median :0.49833   Median :0.48673   Median :0.6267  
##  Mean   :1.395   Mean   :0.49538   Mean   :0.47435   Mean   :0.6279  
##  3rd Qu.:2.000   3rd Qu.:0.65542   3rd Qu.:0.60860   3rd Qu.:0.7302  
##  Max.   :3.000   Max.   :0.86167   Max.   :0.84090   Max.   :0.9725  
##    windspeed           casual         registered        cnt      
##  Min.   :0.02239   Min.   :   2.0   Min.   :  20   Min.   :  22  
##  1st Qu.:0.13495   1st Qu.: 315.5   1st Qu.:2497   1st Qu.:3152  
##  Median :0.18097   Median : 713.0   Median :3662   Median :4548  
##  Mean   :0.19049   Mean   : 848.2   Mean   :3656   Mean   :4504  
##  3rd Qu.:0.23321   3rd Qu.:1096.0   3rd Qu.:4776   3rd Qu.:5956  
##  Max.   :0.50746   Max.   :3410.0   Max.   :6946   Max.   :8714
## Classes 'spec_tbl_df', 'tbl_df', 'tbl' and 'data.frame': 731 obs. of  16 variables:
##  $ instant   : num  1 2 3 4 5 6 7 8 9 10 ...
##  $ dteday    : Date, format: "2011-01-01" "2011-01-02" ...
##  $ season    : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ yr        : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ mnth      : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ holiday   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ weekday   : num  6 0 1 2 3 4 5 6 0 1 ...
##  $ workingday: num  0 0 1 1 1 1 1 0 0 1 ...
##  $ weathersit: num  2 2 1 1 1 1 2 2 1 1 ...
##  $ temp      : num  0.344 0.363 0.196 0.2 0.227 ...
##  $ atemp     : num  0.364 0.354 0.189 0.212 0.229 ...
##  $ hum       : num  0.806 0.696 0.437 0.59 0.437 ...
##  $ windspeed : num  0.16 0.249 0.248 0.16 0.187 ...
##  $ casual    : num  331 131 120 108 82 88 148 68 54 41 ...
##  $ registered: num  654 670 1229 1454 1518 ...
##  $ cnt       : num  985 801 1349 1562 1600 ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   instant = col_double(),
##   ..   dteday = col_date(format = ""),
##   ..   season = col_double(),
##   ..   yr = col_double(),
##   ..   mnth = col_double(),
##   ..   holiday = col_double(),
##   ..   weekday = col_double(),
##   ..   workingday = col_double(),
##   ..   weathersit = col_double(),
##   ..   temp = col_double(),
##   ..   atemp = col_double(),
##   ..   hum = col_double(),
##   ..   windspeed = col_double(),
##   ..   casual = col_double(),
##   ..   registered = col_double(),
##   ..   cnt = col_double()
##   .. )

2 Data Screening

2.1 Data Cleaning

##     instant          dteday               season            yr        
##  Min.   :  1.0   Min.   :2011-01-01   Min.   :1.000   Min.   :0.0000  
##  1st Qu.:183.5   1st Qu.:2011-07-02   1st Qu.:2.000   1st Qu.:0.0000  
##  Median :366.0   Median :2012-01-01   Median :3.000   Median :1.0000  
##  Mean   :366.0   Mean   :2012-01-01   Mean   :2.497   Mean   :0.5007  
##  3rd Qu.:548.5   3rd Qu.:2012-07-01   3rd Qu.:3.000   3rd Qu.:1.0000  
##  Max.   :731.0   Max.   :2012-12-31   Max.   :4.000   Max.   :1.0000  
##       mnth          holiday           weekday        workingday   
##  Min.   : 1.00   Min.   :0.00000   Min.   :0.000   Min.   :0.000  
##  1st Qu.: 4.00   1st Qu.:0.00000   1st Qu.:1.000   1st Qu.:0.000  
##  Median : 7.00   Median :0.00000   Median :3.000   Median :1.000  
##  Mean   : 6.52   Mean   :0.02873   Mean   :2.997   Mean   :0.684  
##  3rd Qu.:10.00   3rd Qu.:0.00000   3rd Qu.:5.000   3rd Qu.:1.000  
##  Max.   :12.00   Max.   :1.00000   Max.   :6.000   Max.   :1.000  
##    weathersit         temp             atemp              hum        
##  Min.   :1.000   Min.   :0.05913   Min.   :0.07907   Min.   :0.0000  
##  1st Qu.:1.000   1st Qu.:0.33708   1st Qu.:0.33784   1st Qu.:0.5200  
##  Median :1.000   Median :0.49833   Median :0.48673   Median :0.6267  
##  Mean   :1.395   Mean   :0.49538   Mean   :0.47435   Mean   :0.6279  
##  3rd Qu.:2.000   3rd Qu.:0.65542   3rd Qu.:0.60860   3rd Qu.:0.7302  
##  Max.   :3.000   Max.   :0.86167   Max.   :0.84090   Max.   :0.9725  
##    windspeed           casual         registered        cnt      
##  Min.   :0.02239   Min.   :   2.0   Min.   :  20   Min.   :  22  
##  1st Qu.:0.13495   1st Qu.: 315.5   1st Qu.:2497   1st Qu.:3152  
##  Median :0.18097   Median : 713.0   Median :3662   Median :4548  
##  Mean   :0.19049   Mean   : 848.2   Mean   :3656   Mean   :4504  
##  3rd Qu.:0.23321   3rd Qu.:1096.0   3rd Qu.:4776   3rd Qu.:5956  
##  Max.   :0.50746   Max.   :3410.0   Max.   :6946   Max.   :8714
##     instant          dteday               season            yr        
##  Min.   :  1.0   Min.   :2011-01-01   Min.   :1.000   Min.   :0.0000  
##  1st Qu.:183.5   1st Qu.:2011-07-02   1st Qu.:2.000   1st Qu.:0.0000  
##  Median :366.0   Median :2012-01-01   Median :3.000   Median :1.0000  
##  Mean   :366.0   Mean   :2012-01-01   Mean   :2.497   Mean   :0.5007  
##  3rd Qu.:548.5   3rd Qu.:2012-07-01   3rd Qu.:3.000   3rd Qu.:1.0000  
##  Max.   :731.0   Max.   :2012-12-31   Max.   :4.000   Max.   :1.0000  
##                                                                       
##       mnth          holiday           weekday        workingday   
##  Min.   : 1.00   Min.   :0.00000   Min.   :0.000   Min.   :0.000  
##  1st Qu.: 4.00   1st Qu.:0.00000   1st Qu.:1.000   1st Qu.:0.000  
##  Median : 7.00   Median :0.00000   Median :3.000   Median :1.000  
##  Mean   : 6.52   Mean   :0.02873   Mean   :2.997   Mean   :0.684  
##  3rd Qu.:10.00   3rd Qu.:0.00000   3rd Qu.:5.000   3rd Qu.:1.000  
##  Max.   :12.00   Max.   :1.00000   Max.   :6.000   Max.   :1.000  
##                                                                   
##    weathersit         temp             atemp              hum        
##  Min.   :1.000   Min.   :0.05913   Min.   :0.07907   Min.   :0.0000  
##  1st Qu.:1.000   1st Qu.:0.33708   1st Qu.:0.33784   1st Qu.:0.5200  
##  Median :1.000   Median :0.49833   Median :0.48673   Median :0.6267  
##  Mean   :1.395   Mean   :0.49538   Mean   :0.47435   Mean   :0.6279  
##  3rd Qu.:2.000   3rd Qu.:0.65542   3rd Qu.:0.60860   3rd Qu.:0.7302  
##  Max.   :3.000   Max.   :0.86167   Max.   :0.84090   Max.   :0.9725  
##                                                                      
##    windspeed           casual         registered        cnt        seasoning  
##  Min.   :0.02239   Min.   :   2.0   Min.   :  20   Min.   :  22   Winter:181  
##  1st Qu.:0.13495   1st Qu.: 315.5   1st Qu.:2497   1st Qu.:3152   Spring:184  
##  Median :0.18097   Median : 713.0   Median :3662   Median :4548   Summer:188  
##  Mean   :0.19049   Mean   : 848.2   Mean   :3656   Mean   :4504   Fall  :178  
##  3rd Qu.:0.23321   3rd Qu.:1096.0   3rd Qu.:4776   3rd Qu.:5956               
##  Max.   :0.50746   Max.   :3410.0   Max.   :6946   Max.   :8714               
##                                                                               
##    year              hol              wd                 working   
##  2011:365   Not Holiday:710   Sunday   :105   Not Working Day:231  
##  2012:366   Holiday    : 21   Monday   :105   Working Day    :500  
##                               Tuesday  :104                        
##                               Wednesday:104                        
##                               Thursday :104                        
##                               Friday   :104                        
##                               Saturday :105                        
##    weather   
##  Good  :463  
##  Cloudy:247  
##  Wet   : 21  
##  Lousy :  0  
##              
##              
## 
## [1] 0
##   [1]  10.268865   7.621839   7.036662   5.961186   6.910391   9.933541
##   [7]   6.573209   7.914417  13.249294   7.005850   7.974819   7.844763
##  [13]   8.157304   8.205320   8.432440   7.821059   8.048934   9.978601
##  [19]   5.440898   4.943166   9.796207  11.895396   9.881564   8.436761
##  [25]   6.301065  12.293055   9.312673   8.848046   8.250943  12.140716
##  [31]   5.876293  12.492898   6.428397   6.757065   6.123505  12.093803
##  [37]   6.791330  10.634334   8.775205   6.501072   6.816131   8.148888
##  [43]   5.906885   6.905365  12.317502   8.550533   5.038033   4.116809
##  [49]   5.289272  26.758594   7.229926   7.212997   5.219142  10.444506
##  [55]   4.263925   7.590403   5.433898   6.302602   9.322686   3.571473
##  [61]   4.987758   8.796769   3.433009   6.346412  16.084742   6.727396
##  [67]   7.982114   4.725667  33.070173   3.038677   4.024918   4.719285
##  [73]   5.670675   2.943045   3.927959   2.263086   4.000514  11.075657
##  [79]   4.846683   4.758604   2.886971   5.683812   6.193291   3.769429
##  [85]   6.786280   6.158850   8.910670   7.518007   3.855954   9.498339
##  [91]   3.632114   3.737260   4.317630  10.146484   8.481624   3.393949
##  [97]   2.121745   5.543472   7.732667   6.629243   6.179487   5.450839
## [103]   5.513799   4.486827   3.620388  13.902969   5.265129   3.173506
## [109]   2.202801   2.321585   6.024551   3.558821   8.468156   5.459034
## [115]   3.027197   6.467859   7.953977   5.512067   2.918392   4.237152
## [121]   4.966565   1.666079   6.439028   5.606799   3.445275   1.535264
## [127]   3.726710   5.608219   1.814527   3.881699   2.280087   2.201580
## [133]   3.924331   7.664745   6.197085   2.991254   5.732616   4.306428
## [139]   3.801729   2.401684   4.085213   4.074839   3.920347   3.033099
## [145]   2.160485   2.863609   2.699888   4.652736   6.387778   7.264360
## [151]   7.472025   5.452593  10.608188   5.751025   6.148943   3.775972
## [157]   4.059807   2.650509   5.723279   8.799229   4.751416   4.716188
## [163]   4.835702   4.572790   4.441395   2.947223   2.278792   2.357211
## [169]   4.979753   5.932689   2.453477   2.578745   3.610236   4.198196
## [175]   3.652590   5.261357   6.750819   3.392420   3.975705   5.240495
## [181]   4.777609  10.125069  10.339580   4.859731   6.547355   4.934761
## [187]   3.456385   4.099776   4.206502   5.414828   5.551392   8.083174
## [193]   6.702264   4.653441   3.805352   1.450712   3.722564   4.762808
## [199]   4.127864   6.667513   7.653632  20.819632  20.582838  17.916988
## [205]  14.241427   8.003351   6.100742  10.803875   6.375060  10.638076
## [211]  11.133052  11.347777   7.197605   7.244595   6.204592   3.074908
## [217]   2.683661   5.964723   8.301764   5.357846   5.882294   9.464976
## [223]   7.821768   8.316538   4.914080   6.384050   2.487541   3.391567
## [229]   4.431332   4.511574   3.475900   4.974900   7.308849   5.571152
## [235]   3.771741   2.660617   4.390226   4.255103  19.583507   7.662607
## [241]   2.863966   3.000974   4.139689   2.059557   2.124743   4.292069
## [247]   4.855955   6.639859  11.143736  10.900613  13.746123   8.791243
## [253]   4.403378   4.367778   3.535963   2.357330   2.237579   3.957761
## [259]   1.578213   3.113690   2.873775   1.369712   4.225604   5.636681
## [265]   8.692296  18.352653   7.069807   9.733930   5.459446   6.706988
## [271]   5.413054   1.594121   1.442891   8.100081   5.850061   4.608499
## [277]   2.115091   2.022631   2.121480   5.931779   6.313588   5.488342
## [283]   6.516203   2.748139   7.791861   6.263515   3.077966   6.228915
## [289]   6.944677   2.188470   2.605056   7.342889  13.679394   2.749242
## [295]   5.311701   4.968088   2.874520   1.924140   2.257336   4.234912
## [301]   3.586054  17.548784   4.567684   4.308093   3.267412   5.149102
## [307]   3.268689   4.937711   6.119885   6.739545   5.797762   5.058706
## [313]   5.673852   4.730894   9.936242   5.501642   8.223062   7.246968
## [319]   2.696257   8.538559   6.909574   8.714448   6.513028   4.756312
## [325]   6.511985   9.945371   9.289923   9.949817   6.148920   7.948875
## [331]   5.585807   3.164121   6.524087   5.518559   6.380082   6.615700
## [337]   8.278445   8.399243   7.115627   9.688213  14.289612   7.154085
## [343]   7.660658   8.842209  14.351253   9.465361   6.642904   7.998825
## [349]   5.547163   6.938479   8.906785   8.609969   5.756857   8.162934
## [355]   7.299315   8.059823   7.909082  11.935060  11.039749  11.705582
## [361]   8.394681  10.136822   8.811444   6.135730   8.126212   6.174793
## [367]   9.337468  11.965149   8.600194   5.874867   4.345681   5.777652
## [373]   5.924424   7.805604   4.439290   8.580019   6.813402   9.500381
## [379]   7.923994   8.503632   6.774590   8.405721  11.432714   6.031868
## [385]   5.632816  11.332054  11.204470  12.242090   9.275000   5.607518
## [391]   8.907399   8.927231   6.022650   8.850759   5.771895   4.879510
## [397]   3.389308   2.958860   3.639823   8.300056   6.029917   4.278301
## [403]   4.314281   5.400849   4.073124   5.369231   9.209784  15.733663
## [409]   6.240262   4.723266   3.216370   6.477719   3.574888   5.208545
## [415]   5.380957   5.005737   3.491918   3.322583   2.909376   4.450742
## [421]  13.629479   6.583306   3.569670   4.639951   5.512074   2.397786
## [427]   2.913671   3.944120   7.561797   3.587537   4.255811   6.184778
## [433]  16.492058  10.603751   7.150304   4.947144   2.882991   3.269914
## [439]   4.516336   3.174136   6.108342  13.266372   9.173940   4.767288
## [445]   6.272719   7.767375   8.885577   9.581037   7.898925  11.059495
## [451]  10.181544   7.785126   4.731417   6.988142   4.326000  10.702165
## [457]   6.174926   6.019039   7.444213   4.021949   5.812995   7.547404
## [463]  11.571407   9.306195   9.633731   4.001969   4.331263   4.391318
## [469]   5.130245   8.014529   6.146503   6.519413   7.778893   1.601775
## [475]   5.901418   6.140465   8.572434  11.651766   6.709550   3.663755
## [481]   5.353028   2.820001   9.119990   5.027770   6.106647   2.216183
## [487]   1.596773   4.217175   4.107041   2.896807   6.673716   5.717424
## [493]   3.660680   4.813924   2.208419   6.499005   6.350635   7.051388
## [499]   4.128282   3.836382   2.891967   4.733591   4.559230   5.096589
## [505]  10.172500   6.165688   3.651751   3.484066   3.467486   3.608533
## [511]   4.231415   5.916637   5.638795   5.153360   5.287159   3.276443
## [517]   3.793119   3.148853   7.671124   6.081806   5.613143   3.515235
## [523]   4.602787   3.337066   4.608621   7.748353   5.981432   2.875169
## [529]   4.465856   8.769781   4.917802   3.520963   5.971746   4.777497
## [535]   2.010945   2.750170   4.420095   5.235508   3.485904   7.788161
## [541]   7.163746   5.553587   9.949545   7.000550   6.220204   7.804337
## [547]   6.595118   7.605565   6.412833   6.453135   6.349348   6.275914
## [553]   7.617974  11.610919  11.270038   2.474216   2.307657   3.795250
## [559]   3.966133   6.786175   4.875203   4.787745   3.066128   5.901827
## [565]   4.572885   2.831205   4.806558   6.411359   7.256109   2.914657
## [571]   4.003544   6.464742   6.475949   3.283073   4.832582   4.271537
## [577]   2.684221   3.116134   3.280903   3.029101   3.685822   7.391912
## [583]   8.368574   2.923117   3.334673   3.595032   2.966273   3.049723
## [589]   4.919233   5.603591   3.425234   2.367381   2.758219   4.581097
## [595] 450.050485   6.540250   5.054837   2.415110   4.246644   4.472428
## [601]   5.222983   5.076309   4.923461   7.144335   2.928030   2.973791
## [607]   4.058973   5.031963   4.338455   5.288554   6.856560   4.962812
## [613]   4.787191   4.471263   3.174633   3.762909   8.186393   7.677452
## [619]   5.907805   5.270687   4.050751   4.700427   4.748460  10.271302
## [625]   6.222528   3.029307  12.167883   4.997935   4.571943   5.048198
## [631]  10.903755   8.576922   4.802408   5.985962   4.995341   3.194906
## [637]   3.280681  10.209777   5.113222   3.986309   5.435661   7.531062
## [643]   4.072965   5.111243  10.876956   4.487625   5.721253   5.185781
## [649]   5.525442   7.121121   6.737725   8.313892   7.804253   5.747032
## [655]   5.673471   6.491556   7.703462   2.928609   8.865473   6.183501
## [661]   5.443059   4.702919   5.170487   5.821725   6.309736  10.383800
## [667]  13.793409  17.888839   7.158404   3.960292   5.030881   6.989753
## [673]   8.328218   6.437192   6.418924   6.731885   9.274383  12.641702
## [679]   5.584143   9.067901   7.578236   6.053964   9.159463   6.639162
## [685]   5.095469   5.360773   7.018331   6.273943   4.755932   5.524317
## [691]   5.149771  11.289732   4.684932  15.974964   9.927605   9.466132
## [697]   7.200722   6.410434   6.909472   8.531541  11.020218   8.189847
## [703]   6.278147   5.570924   9.450983   8.380455   6.513444  11.206186
## [709]   8.750152   8.636602   8.636035   6.900323   7.830187   7.480778
## [715]   7.745413   7.970823   7.724280   5.233610   5.695773   5.096564
## [721]  12.378674  19.464526  11.816352  12.147030   9.894699  15.553442
## [727]  13.485708   6.979471  11.424271  15.251901   7.980102
## [1] 24.32189
##    Mode   FALSE    TRUE 
## logical       3     728
## Classes 'tbl_df', 'tbl' and 'data.frame':    728 obs. of  7 variables:
##  $ mnth      : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ workingday: num  0 0 1 1 1 1 1 0 0 1 ...
##  $ temp      : num  0.344 0.363 0.196 0.2 0.227 ...
##  $ atemp     : num  0.364 0.354 0.189 0.212 0.229 ...
##  $ hum       : num  0.806 0.696 0.437 0.59 0.437 ...
##  $ windspeed : num  0.16 0.249 0.248 0.16 0.187 ...
##  $ cnt       : num  985 801 1349 1562 1600 ...

2.2 Parametric Test

##                    mnth   workingday        temp       atemp         hum
## mnth        1.000000000 -0.005900951  0.22020534  0.22745863  0.22220369
## workingday -0.005900951  1.000000000  0.05265981  0.05218228  0.02432705
## temp        0.220205335  0.052659810  1.00000000  0.99170155  0.12696294
## atemp       0.227458630  0.052182275  0.99170155  1.00000000  0.13998806
## hum         0.222203691  0.024327046  0.12696294  0.13998806  1.00000000
## windspeed  -0.207501752 -0.018796487 -0.15794412 -0.18364297 -0.24848910
## cnt         0.279977112  0.061156063  0.62749401  0.63106570 -0.10065856
##              windspeed         cnt
## mnth       -0.20750175  0.27997711
## workingday -0.01879649  0.06115606
## temp       -0.15794412  0.62749401
## atemp      -0.18364297  0.63106570
## hum        -0.24848910 -0.10065856
## windspeed   1.00000000 -0.23454500
## cnt        -0.23454500  1.00000000
## corrplot 0.84 loaded

##            m wr t a h wn c
## mnth       1              
## workingday   1            
## temp            1         
## atemp           B 1       
## hum                 1     
## windspeed             1   
## cnt             , ,      1
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1
## 
## Call:
## lm(formula = random ~ ., data = nocat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.5232 -2.6629 -0.5341  1.8824 17.6860 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.717e+00  9.966e-01   7.743 3.28e-14 ***
## mnth         1.358e-03  4.235e-02   0.032    0.974    
## workingday  -3.334e-01  2.908e-01  -1.147    0.252    
## temp         5.896e+00  5.851e+00   1.008    0.314    
## atemp       -7.475e+00  6.621e+00  -1.129    0.259    
## hum          7.892e-01  1.055e+00   0.748    0.455    
## windspeed   -1.412e+00  1.903e+00  -0.742    0.458    
## cnt         -9.291e-05  9.755e-05  -0.952    0.341    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.644 on 723 degrees of freedom
## Multiple R-squared:  0.01057,    Adjusted R-squared:  0.0009884 
## F-statistic: 1.103 on 7 and 723 DF,  p-value: 0.3591

##        mnth  workingday        temp       atemp         hum   windspeed 
## -0.01156011 -0.79187422 -0.05615175 -0.13708890  0.06051464  0.62476208 
##         cnt 
## -0.04455265
##       mnth workingday       temp      atemp        hum  windspeed        cnt 
##   1.792561   1.627065   1.880405   2.015374   2.465593   3.174248   2.191819

3 Exploratory Data Analysis

##  Date[1:731], format: "2011-01-01" "2011-01-02" "2011-01-03" "2011-01-04" "2011-01-05" ...
##   Winter   Spring   Summer     Fall 
## 2604.133 4992.332 5644.303 4728.163

##     2011     2012 
## 3405.762 5599.934

##        1        2        3        4        5        6        7        8 
## 2176.339 2655.298 3692.258 4484.900 5349.774 5772.367 5563.677 5664.419 
##        9       10       11       12 
## 5766.517 5199.226 4247.183 3403.806

## Not Holiday     Holiday 
##    4527.104    3735.000

##    Sunday    Monday   Tuesday Wednesday  Thursday    Friday  Saturday 
##  4228.829  4338.124  4510.663  4548.538  4667.260  4690.288  4550.543

## Not Working Day     Working Day 
##        4330.169        4584.820

##     Good   Cloudy      Wet    Lousy 
## 4876.786 4035.862 1803.286       NA

## 
##  Very Low       Low    Medium      High Very High 
##        34       227       216       238        16
##  Very Low       Low    Medium      High Very High 
##  1543.235  3178.546  5011.208  5714.340  4765.312

## 
## 0.0-0.2 0.2-0.4 0.4-0.6 0.6-0.8 0.8-1.0 
##       1      28     292     317      92
##  0.0-0.2  0.2-0.4  0.4-0.6  0.6-0.8  0.8-1.0 
## 1635.000 4454.429 4601.185 4760.148 3404.174

## 
## 0.0223917 0.0423042 0.0454042 0.0454083   0.04665  0.047275 0.0503792 0.0528708 
##         1         1         1         1         1         1         1         1 
##  0.053213  0.057225 0.0578458 0.0584708 0.0597042 0.0609583 0.0615708 0.0621958 
##         1         1         1         1         1         1         1         1 
## 0.0622083   0.06345 0.0640708 0.0659292 0.0665417 0.0665458 0.0684208 0.0690375 
##         1         2         1         1         1         1         1         1 
## 0.0702833 0.0721458 0.0727708 0.0727792 0.0733958 0.0739826 0.0746375 0.0771167 
##         1         1         1         1         1         1         1         1 
##  0.077125 0.0772304 0.0783667 0.0783833   0.08085 0.0814792 0.0814833 0.0820917 
##         1         1         1         1         1         1         1         1 
## 0.0827167 0.0827208  0.082725 0.0833333 0.0833458 0.0839583 0.0839625  0.083975 
##         1         2         1         1         1         1         1         1 
## 0.0845958   0.08645  0.088913 0.0895583 0.0895652 0.0901833 0.0908042 0.0908083 
##         1         1         1         1         1         1         1         1 
##  0.091425 0.0920542 0.0926667 0.0939208  0.094113 0.0945333 0.0945458 0.0957833 
##         1         2         1         1         1         1         1         1 
## 0.0964042 0.0970208 0.0982583 0.0988958    0.0989 0.0995125  0.100133  0.100742 
##         1         1         1         1         1         1         1         1 
##  0.100754  0.101371  0.101379     0.102  0.102608  0.103246  0.103863  0.104467 
##         1         1         1         2         1         1         1         1 
##  0.104475   0.10635  0.106354  0.107588  0.108213   0.10855  0.110087    0.1107 
##         1         3         1         1         1         1         1         3 
##  0.110704  0.110708  0.111329  0.112562  0.113187  0.113192  0.113812  0.113817 
##         1         1         1         1         1         1         1         1 
##  0.113837  0.114429  0.115054  0.115062  0.115522  0.115671    0.1163  0.116908 
##         1         1         1         2         1         1         1         2 
##  0.116929  0.117537  0.117546  0.117562  0.118167  0.118171  0.118787  0.118792 
##         1         1         1         1         2         1         1         3 
##  0.119408  0.119412  0.120642   0.12065  0.121271  0.121896  0.122132  0.122512 
##         1         1         1         2         1         2         1         2 
##  0.123133  0.123142    0.1233  0.123767  0.124375  0.124379  0.124383  0.125008 
##         1         1         1         1         1         2         1         1 
##  0.125013  0.125248  0.125621  0.125629  0.126237  0.126258  0.126548  0.126871 
##         1         1         1         1         1         1         1         1 
##  0.126883    0.1275  0.127839  0.128125  0.128733  0.129354  0.129796  0.129975 
##         1         1         1         1         1         2         1         1 
##  0.129979  0.129987    0.1306  0.131221  0.131225  0.131229  0.131846  0.132463 
##         1         1         2         2         1         1         1         1 
##  0.132467  0.133083    0.1331  0.133696  0.133721  0.134329  0.134337  0.134342 
##         1         2         1         1         2         1         1         1 
##   0.13495  0.134954  0.134958  0.135571  0.135583  0.136212  0.136817  0.136829 
##         2         3         1         1         1         1         3         1 
##  0.136926  0.137442  0.138054  0.138058  0.138067  0.138683  0.138692  0.139308 
##         1         1         1         1         1         1         1         1 
##  0.139929   0.14055  0.140554  0.141162  0.141179  0.141787  0.141796    0.1418 
##         1         2         1         1         2         1         2         1 
##  0.141804  0.142122  0.142404  0.142421  0.143029  0.143042  0.143667  0.143679 
##         1         1         1         1         1         1         1         1 
##  0.144283  0.144287  0.144904  0.145365  0.145525  0.146133  0.146142  0.146763 
##         1         1         2         1         1         1         2         1 
##  0.146767  0.146775  0.147379  0.147392  0.148008  0.148017  0.148021  0.148629 
##         1         2         1         1         1         1         1         1 
##  0.148642  0.149871  0.149879  0.149883    0.1505  0.151121  0.151733  0.151737 
##         1         1         1         3         1         2         1         1 
##  0.151742  0.152979  0.152987  0.152992  0.153608  0.153617    0.1538  0.154229 
##         2         1         1         2         1         1         1         1 
##  0.154233  0.154846   0.15485  0.155091  0.155471  0.155475  0.156096    0.1561 
##         1         1         1         1         2         1         1         1 
##  0.156717  0.157346   0.15735  0.157963  0.157971  0.157975   0.15833    0.1592 
##         1         1         2         1         1         1         1         1 
##  0.159825  0.160296  0.160446   0.16045  0.161071  0.161079  0.162312  0.162317 
##         1         1         1         1         2         2         1         1 
##  0.162937  0.162938  0.163554  0.163567  0.164179  0.164183  0.164187  0.164796 
##         1         1         1         2         1         1         1         1 
##    0.1648  0.164813  0.165417  0.165425  0.165429  0.166054  0.166658  0.166667 
##         1         1         1         1         1         1         1         3 
##  0.167283    0.1673  0.167304  0.167908  0.167912  0.168529  0.168533  0.168537 
##         1         1         1         1         3         1         2         1 
##  0.168726  0.169158  0.169171  0.169771  0.169779  0.170396  0.171025  0.171638 
##         2         1         1         1         1         1         2         1 
##  0.171646   0.17165   0.17197  0.172262  0.172267  0.172883  0.172888  0.172896 
##         1         1         1         1         1         1         1         2 
##  0.173513  0.173517  0.174129  0.174138  0.174746  0.174754  0.174758  0.175379 
##         1         1         2         1         1         1         1         1 
##  0.175383  0.175996     0.176  0.176617  0.176625   0.17725  0.177867  0.178479 
##         1         1         1         2         1         1         1         1 
##  0.178483  0.178496  0.179108  0.179117  0.179721  0.179725  0.179729  0.180967 
##         1         1         1         1         1         1         1         1 
##  0.180975  0.181596    0.1816  0.182213  0.182221  0.182833  0.182842  0.183454 
##         2         1         1         1         1         1         1         1 
##  0.183463  0.183471  0.184087  0.184092    0.1843  0.184309  0.184696    0.1847 
##         1         1         1         1         1         1         1         1 
##  0.185312  0.185325  0.185333   0.18595  0.186562  0.186571    0.1869  0.187183 
##         1         1         1         1         1         1         1         1 
##  0.187187  0.187192  0.187552  0.187808  0.187821  0.188433   0.18845  0.188839 
##         1         2         1         2         1         1         1         1 
##  0.189062  0.189067  0.189667  0.189675  0.189679    0.1903  0.190304  0.190308 
##         1         2         1         1         1         1         1         1 
##  0.190913  0.190917  0.190925  0.190929  0.191542  0.192167  0.192175  0.192748 
##         1         1         1         1         1         1         2         1 
##  0.192783  0.193417  0.194017  0.194029  0.194037  0.195267  0.195279  0.195683 
##         1         1         1         1         1         1         1         1 
##  0.195904  0.196521  0.197146   0.19715  0.197763  0.198992  0.199625  0.199633 
##         1         1         1         1         1         1         1         1 
##  0.199638  0.199642  0.200254  0.200258  0.200875  0.201487  0.201492   0.20275 
##         1         1         1         2         1         1         1         1 
##  0.203117  0.203346  0.203367  0.205229  0.205717  0.205846   0.20585  0.205854 
##         1         1         1         1         1         1         1         1 
##  0.206467  0.206471  0.206475  0.206479  0.207092  0.207713  0.207721  0.208317 
##         1         1         1         1         2         2         1         1 
##  0.208342  0.208954  0.208967  0.209571  0.209575  0.209579  0.210821  0.210829 
##         1         2         1         2         1         1         1         1 
##  0.210833  0.211454  0.212062  0.212204  0.212692  0.212696  0.213009    0.2133 
##         1         2         1         1         1         1         1         1 
##  0.213938  0.214546  0.214558  0.215171  0.215175  0.215792  0.215804  0.216412 
##         1         1         1         1         1         2         1         1 
##  0.216425  0.217646  0.219521  0.219529   0.22015  0.220154  0.220158  0.220775 
##         1         1         1         1         1         1         2         2 
##  0.221396    0.2214  0.221404  0.221935  0.222013  0.222021  0.222025  0.222587 
##         1         1         1         1         1         1         1         1 
##  0.222633  0.222642  0.223235  0.223258  0.223267  0.223883  0.224496  0.225117 
##         1         1         1         1         1         1         2         1 
##  0.225129   0.22575  0.225754  0.226375  0.226987  0.226992  0.226996  0.227604 
##         2         2         1         1         1         1         1         1 
##  0.227612  0.228246   0.22825  0.228858  0.229083  0.229475  0.229479  0.230092 
##         1         1         1         3         1         1         1         1 
##  0.230104  0.230721  0.230725  0.231017  0.231354  0.231358  0.232583  0.232596 
##         1         1         2         1         1         1         1         1 
##   0.23297  0.233204  0.233208  0.233221  0.233842  0.234261  0.234471  0.235067 
##         1         1         1         1         1         1         1         1 
##  0.235075  0.235092  0.235692  0.236321  0.236325  0.236329  0.236937   0.23695 
##         1         1         1         2         1         1         2         1 
##  0.237562  0.237563  0.237567  0.238804  0.238813  0.239465   0.24005  0.240058 
##         1         1         1         1         1         1         1         1 
##  0.240063  0.240667  0.240679  0.241925  0.243167  0.243339  0.243787    0.2444 
##         1         1         1         1         1         1         1         1 
##  0.244408  0.245033    0.2466  0.247521   0.24815  0.248309  0.248539  0.248754 
##         1         1         1         1         1         1         1         1 
##  0.249375  0.249383  0.250496  0.250617  0.251258  0.251791  0.251871  0.253108 
##         1         1         1         2         1         1         1         1 
##  0.253112  0.253121  0.253733  0.254367  0.257458  0.258083  0.258092  0.258708 
##         1         1         1         1         1         1         1         1 
##  0.258713  0.260575  0.260883  0.261817  0.261821  0.261877  0.263063  0.264308 
##         1         1         1         1         1         1         1         1 
##  0.264925  0.266175  0.266804  0.268025  0.268033  0.268042  0.269283  0.270529 
##         1         2         1         1         1         1         1         1 
##  0.270604  0.271146  0.271158  0.271775  0.271779  0.273629  0.274246  0.274871 
##         1         1         1         1         1         1         1         1 
##  0.274879   0.27675  0.277354  0.277752  0.278612  0.281104  0.281717  0.281721 
##         1         1         1         1         1         1         1         1 
##  0.282337  0.283583  0.283587  0.284813  0.284829  0.284833  0.288783  0.289686 
##         1         1         1         1         1         1         1         1 
##  0.289796  0.290421  0.290429  0.291374  0.291671  0.292287  0.292296   0.29385 
##         1         1         1         1         1         1         1         1 
##  0.293961  0.295274  0.295392    0.2954  0.296029  0.296037  0.300383  0.300388 
##         1         1         1         1         1         2         1         1 
##     0.301  0.303496  0.304108  0.304627  0.304659   0.30535  0.305362  0.306596 
##         1         2         1         1         1         1         1         1 
##  0.307833  0.307846  0.312139    0.3122  0.314063  0.314675  0.316546   0.31965 
##         1         1         1         1         1         1         1         1 
##  0.320908  0.324021  0.324474  0.325258    0.3265  0.328996  0.329665  0.334571 
##         1         1         1         1         1         1         1         1 
##  0.335825  0.340808  0.341352  0.342046  0.342667  0.343279  0.343287  0.343943 
##         1         1         1         1         2         1         1         1 
##  0.344546  0.345779  0.346539  0.347633  0.347642  0.347835   0.34913  0.350133 
##         1         1         1         1         1         1         1         1 
##  0.350754  0.351371  0.353242  0.357587  0.358196    0.3582   0.36195  0.365671 
##         1         1         1         1         1         1         2         1 
##  0.368167  0.374383  0.375617  0.376871  0.378108  0.385571  0.386821  0.388067 
##         1         1         1         1         1         1         1         1 
##  0.398008  0.407346  0.409212    0.4148  0.415429  0.417908  0.421642  0.422275 
##         1         1         1         1         1         1         1         1 
##  0.441563  0.507463 
##         1         1
##  Very Low       Low    Medium      High Very High 
##  4840.356  4828.333  4239.558  3385.597  3180.625

4 Correlation Analysis

4.1 Correlation

## # A tibble: 6 x 11
##   season    yr  mnth holiday weekday workingday weathersit  temp atemp   hum
##    <dbl> <dbl> <dbl>   <dbl>   <dbl>      <dbl>      <dbl> <dbl> <dbl> <dbl>
## 1      1     0     1       0       6          0          2 0.344 0.364 0.806
## 2      1     0     1       0       0          0          2 0.363 0.354 0.696
## 3      1     0     1       0       1          1          1 0.196 0.189 0.437
## 4      1     0     1       0       2          1          1 0.2   0.212 0.590
## 5      1     0     1       0       3          1          1 0.227 0.229 0.437
## 6      1     0     1       0       4          1          1 0.204 0.233 0.518
## # … with 1 more variable: windspeed <dbl>
## Classes 'tbl_df', 'tbl' and 'data.frame':    731 obs. of  11 variables:
##  $ season    : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ yr        : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ mnth      : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ holiday   : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ weekday   : num  6 0 1 2 3 4 5 6 0 1 ...
##  $ workingday: num  0 0 1 1 1 1 1 0 0 1 ...
##  $ weathersit: num  2 2 1 1 1 1 2 2 1 1 ...
##  $ temp      : num  0.344 0.363 0.196 0.2 0.227 ...
##  $ atemp     : num  0.364 0.354 0.189 0.212 0.229 ...
##  $ hum       : num  0.806 0.696 0.437 0.59 0.437 ...
##  $ windspeed : num  0.16 0.249 0.248 0.16 0.187 ...

4.2 Hypothesis Test

## 
##  Pearson's product-moment correlation
## 
## data:  day$weathersit and day$season
## t = 0.51879, df = 729, p-value = 0.6041
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.05337693  0.09159703
## sample estimates:
##        cor 
## 0.01921103
## 
##  Pearson's product-moment correlation
## 
## data:  day$temp and day$season
## t = 9.5776, df = 729, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2683056 0.3971994
## sample estimates:
##       cor 
## 0.3343149
## 
##  Pearson's product-moment correlation
## 
## data:  day$hum and day$season
## t = 5.6679, df = 729, p-value = 2.083e-08
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1349415 0.2738783
## sample estimates:
##       cor 
## 0.2054448
## 
##  Pearson's product-moment correlation
## 
## data:  day$windspeed and day$season
## t = -6.3531, df = 729, p-value = 3.714e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2966332 -0.1591765
## sample estimates:
##        cor 
## -0.2290463
## 
##  Pearson's product-moment correlation
## 
## data:  day$hum and day$windspeed
## t = -6.9265, df = 729, p-value = 9.488e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3153210 -0.1792046
## sample estimates:
##        cor 
## -0.2484891
## 
##  Pearson's product-moment correlation
## 
## data:  day1$season and day1$mnth
## t = 40.404, df = 729, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8076184 0.8525527
## sample estimates:
##       cor 
## 0.8314401
## 
##  Pearson's product-moment correlation
## 
## data:  day$weathersit and day$hum
## t = 19.784, df = 729, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.5417497 0.6362877
## sample estimates:
##       cor 
## 0.5910446
## 
##  Pearson's product-moment correlation
## 
## data:  day$hum and day1$mnth
## t = 6.1533, df = 729, p-value = 1.251e-09
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1521415 0.2900439
## sample estimates:
##       cor 
## 0.2222037
## 
##  Pearson's product-moment correlation
## 
## data:  day$holiday and day$workingday
## t = -7.0614, df = 729, p-value = 3.851e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.3196711 -0.1838829
## sample estimates:
##        cor 
## -0.2530227
##              Df    Sum Sq   Mean Sq F value Pr(>F)    
## tempbucket    4 1.102e+09 275540185   122.2 <2e-16 ***
## Residuals   726 1.637e+09   2255337                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = cnt ~ tempbucket, data = day)
## 
## $tempbucket
##                         diff        lwr       upr     p adj
## Low-Very Low       1635.3110   880.0890 2390.5329 0.0000000
## Medium-Very Low    3467.9730  2710.2501 4225.6959 0.0000000
## High-Very Low      4171.1050  3418.1600 4924.0500 0.0000000
## Very High-Very Low 3222.0772  1977.0114 4467.1430 0.0000000
## Medium-Low         1832.6621  1442.2989 2223.0252 0.0000000
## High-Low           2535.7941  2154.7881 2916.8001 0.0000000
## Very High-Low      1586.7662   524.4913 2649.0412 0.0004696
## High-Medium         703.1320   317.1924 1089.0716 0.0000078
## Very High-Medium   -245.8958 -1309.9503  818.1586 0.9698722
## Very High-High     -949.0278 -2009.6852  111.6296 0.1042759
## 
## Not Holiday     Holiday 
##         710          21
## Loading required package: BayesFactor
## Loading required package: coda
## Loading required package: Matrix
## ************
## Welcome to BayesFactor 0.9.12-4.2. If you have questions, please contact Richard Morey (richarddmorey@gmail.com).
## 
## Type BFManual() to open the manual.
## ************
## Response variable: numerical
## Explanatory variable: categorical (2 levels) 
## n_Not Holiday = 710, y_bar_Not Holiday = 4527.1042, s_Not Holiday = 1929.0139
## n_Holiday = 21, y_bar_Holiday = 3735, s_Holiday = 2103.3507
## H0: mu_Not Holiday =  mu_Holiday
## HA: mu_Not Holiday != mu_Holiday
## t = 1.7047, df = 20
## p_value = 0.1037

##              Df    Sum Sq   Mean Sq F value Pr(>F)    
## seasoning     3 9.506e+08 316865289   128.8 <2e-16 ***
## Residuals   727 1.789e+09   2460715                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = cnt ~ seasoning, data = day)
## 
## $seasoning
##                    diff        lwr       upr     p adj
## Spring-Winter 2388.1989  1965.3325 2811.0653 0.0000000
## Summer-Winter 3040.1706  2619.5409 3460.8003 0.0000000
## Fall-Winter   2124.0303  1697.6444 2550.4163 0.0000000
## Summer-Spring  651.9717   233.0927 1070.8507 0.0003925
## Fall-Spring   -264.1686  -688.8276  160.4904 0.3781913
## Fall-Summer   -916.1403 -1338.5720 -493.7085 0.0000002
##              Df    Sum Sq  Mean Sq F value Pr(>F)    
## day$mnth     11 1.070e+09 97290206    41.9 <2e-16 ***
## Residuals   719 1.669e+09  2321757                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## 
## Not Working Day     Working Day 
##             231             500
## Response variable: numerical
## Explanatory variable: categorical (2 levels) 
## n_Not Working Day = 231, y_bar_Not Working Day = 4330.1688, s_Not Working Day = 2052.1412
## n_Working Day = 500, y_bar_Working Day = 4584.82, s_Working Day = 1878.4156
## H0: mu_Not Working Day =  mu_Working Day
## HA: mu_Not Working Day < mu_Working Day
## t = -1.6014, df = 230
## p_value = 0.0553

##              Df    Sum Sq Mean Sq F value Pr(>F)
## wd            6 1.766e+07 2943170   0.783  0.583
## Residuals   724 2.722e+09 3759498

5 Regression Modeling

## Warning in summary.lm(actual): essentially perfect fit: summary may be
## unreliable
## 
## Call:
## lm(formula = cnt ~ ., data = day)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -6.083e-11 -4.270e-13 -3.000e-14  4.150e-13  4.238e-11 
## 
## Coefficients: (8 not defined because of singularities)
##                       Estimate Std. Error    t value Pr(>|t|)    
## (Intercept)         -2.134e-12  1.500e-12 -1.423e+00  0.15511    
## instant             -8.777e-16  1.329e-14 -6.600e-02  0.94736    
## dteday                      NA         NA         NA       NA    
## season               5.533e-14  2.694e-13  2.050e-01  0.83731    
## yr                  -1.582e-12  4.909e-12 -3.220e-01  0.74725    
## mnth2                1.468e-13  7.235e-13  2.030e-01  0.83923    
## mnth3               -1.428e-12  1.059e-12 -1.349e+00  0.17791    
## mnth4               -2.677e-12  1.562e-12 -1.714e+00  0.08703 .  
## mnth5               -2.323e-12  1.925e-12 -1.207e+00  0.22791    
## mnth6               -5.732e-12  2.292e-12 -2.501e+00  0.01261 *  
## mnth7               -4.848e-12  2.697e-12 -1.798e+00  0.07268 .  
## mnth8               -5.073e-12  3.054e-12 -1.661e+00  0.09717 .  
## mnth9               -3.818e-12  3.389e-12 -1.126e+00  0.26038    
## mnth10              -3.547e-12  3.792e-12 -9.350e-01  0.34997    
## mnth11              -3.050e-12  4.169e-12 -7.320e-01  0.46464    
## mnth12              -2.842e-12  4.513e-12 -6.300e-01  0.52904    
## holiday              3.279e-13  8.316e-13  3.940e-01  0.69344    
## weekday             -2.238e-13  7.305e-14 -3.063e+00  0.00228 ** 
## workingday           1.580e-12  5.217e-13  3.028e+00  0.00255 ** 
## weathersit           1.383e-12  4.721e-13  2.929e+00  0.00351 ** 
## temp                 1.178e-11  6.281e-12  1.876e+00  0.06114 .  
## atemp               -4.200e-12  6.176e-12 -6.800e-01  0.49675    
## hum                  1.735e-12  2.452e-12  7.080e-01  0.47927    
## windspeed           -1.476e-12  4.642e-12 -3.180e-01  0.75064    
## casual               1.000e+00  3.526e-16  2.836e+15  < 2e-16 ***
## registered           1.000e+00  2.085e-16  4.797e+15  < 2e-16 ***
## seasoningSpring      1.062e-13  7.006e-13  1.520e-01  0.87959    
## seasoningSummer     -1.518e-14  7.338e-13 -2.100e-02  0.98350    
## seasoningFall               NA         NA         NA       NA    
## year2012                    NA         NA         NA       NA    
## holHoliday                  NA         NA         NA       NA    
## wdMonday            -7.558e-13  5.297e-13 -1.427e+00  0.15405    
## wdTuesday           -7.001e-13  4.899e-13 -1.429e+00  0.15344    
## wdWednesday         -2.964e-13  4.657e-13 -6.360e-01  0.52471    
## wdThursday          -8.658e-14  4.459e-13 -1.940e-01  0.84610    
## wdFriday                    NA         NA         NA       NA    
## wdSaturday                  NA         NA         NA       NA    
## workingWorking Day          NA         NA         NA       NA    
## weatherCloudy       -1.936e-13  4.414e-13 -4.390e-01  0.66112    
## weatherWet                  NA         NA         NA       NA    
## tempbucketLow       -8.291e-13  7.549e-13 -1.098e+00  0.27248    
## tempbucketMedium    -9.331e-13  1.081e-12 -8.640e-01  0.38814    
## tempbucketHigh      -1.217e-12  1.390e-12 -8.760e-01  0.38139    
## tempbucketVery High -1.033e-12  1.827e-12 -5.660e-01  0.57183    
## humbucket0.4-0.6    -5.317e-13  7.379e-13 -7.210e-01  0.47141    
## humbucket0.6-0.8    -8.779e-13  9.996e-13 -8.780e-01  0.38012    
## humbucket0.8-1.0    -2.625e-12  1.341e-12 -1.958e+00  0.05069 .  
## windbucketLow       -1.740e-13  5.422e-13 -3.210e-01  0.74831    
## windbucketMedium     2.412e-13  8.657e-13  2.790e-01  0.78058    
## windbucketHigh       3.773e-14  1.321e-12  2.900e-02  0.97722    
## windbucketVery High  2.852e-14  1.961e-12  1.500e-02  0.98840    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.096e-12 on 686 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 6.747e+30 on 42 and 686 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr, data = traindata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5608.2 -1268.2   321.7  1252.9  3083.8 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3423.82      94.08   36.39   <2e-16 ***
## yr           2206.42     131.27   16.81   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1586 on 582 degrees of freedom
## Multiple R-squared:  0.3268, Adjusted R-squared:  0.3256 
## F-statistic: 282.5 on 1 and 582 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth, data = traindata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6195.3  -476.8   159.8   665.1  3568.1 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1104.15     164.60   6.708 4.76e-11 ***
## yr           2198.32      88.47  24.849  < 2e-16 ***
## mnth2         412.40     223.38   1.846   0.0654 .  
## mnth3        1491.43     221.22   6.742 3.84e-11 ***
## mnth4        2419.65     223.43  10.829  < 2e-16 ***
## mnth5        3143.18     218.93  14.357  < 2e-16 ***
## mnth6        3514.70     222.33  15.808  < 2e-16 ***
## mnth7        3378.06     216.93  15.572  < 2e-16 ***
## mnth8        3505.09     218.96  16.008  < 2e-16 ***
## mnth9        3447.92     218.93  15.749  < 2e-16 ***
## mnth10       2914.80     215.97  13.496  < 2e-16 ***
## mnth11       1948.33     225.88   8.626  < 2e-16 ***
## mnth12       1309.06     215.97   6.061 2.45e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1065 on 571 degrees of freedom
## Multiple R-squared:  0.7018, Adjusted R-squared:  0.6955 
## F-statistic:   112 on 12 and 571 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed, data = traindata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5475.2  -513.2   155.3   643.2  3195.1 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1961.39     203.86   9.621  < 2e-16 ***
## yr           2191.46      85.26  25.702  < 2e-16 ***
## mnth2         407.83     215.27   1.894   0.0587 .  
## mnth3        1462.35     213.24   6.858 1.82e-11 ***
## mnth4        2477.12     215.49  11.495  < 2e-16 ***
## mnth5        3003.50     212.02  14.166  < 2e-16 ***
## mnth6        3391.75     215.05  15.772  < 2e-16 ***
## mnth7        3161.99     211.53  14.948  < 2e-16 ***
## mnth8        3298.10     213.27  15.465  < 2e-16 ***
## mnth9        3228.15     213.52  15.119  < 2e-16 ***
## mnth10       2725.09     210.05  12.973  < 2e-16 ***
## mnth11       1790.61     218.95   8.178 1.88e-15 ***
## mnth12       1151.76     209.45   5.499 5.78e-08 ***
## windspeed   -3854.69     575.76  -6.695 5.18e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1027 on 570 degrees of freedom
## Multiple R-squared:  0.7235, Adjusted R-squared:  0.7172 
## F-statistic: 114.7 on 13 and 570 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum, data = traindata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4826.9  -489.2   135.4   602.8  3407.1 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3593.95     279.92  12.839  < 2e-16 ***
## yr           2104.14      81.57  25.797  < 2e-16 ***
## mnth2         466.95     204.25   2.286   0.0226 *  
## mnth3        1548.36     202.47   7.647 8.79e-14 ***
## mnth4        2549.07     204.52  12.464  < 2e-16 ***
## mnth5        3279.85     203.93  16.083  < 2e-16 ***
## mnth6        3445.25     204.01  16.888  < 2e-16 ***
## mnth7        3234.08     200.77  16.109  < 2e-16 ***
## mnth8        3464.55     203.27  17.044  < 2e-16 ***
## mnth9        3609.10     207.90  17.360  < 2e-16 ***
## mnth10       3055.65     203.34  15.027  < 2e-16 ***
## mnth11       1962.02     208.69   9.402  < 2e-16 ***
## mnth12       1393.71     200.85   6.939 1.08e-11 ***
## windspeed   -4743.62     556.94  -8.517  < 2e-16 ***
## hum         -2506.40     310.83  -8.064 4.40e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 973.5 on 569 degrees of freedom
## Multiple R-squared:  0.7519, Adjusted R-squared:  0.7458 
## F-statistic: 123.2 on 14 and 569 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum + temp, data = traindata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4454.8  -369.1   118.3   580.2  2552.1 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2721.72     269.31  10.106  < 2e-16 ***
## yr           1994.76      75.39  26.459  < 2e-16 ***
## mnth2         119.58     189.87   0.630 0.529080    
## mnth3         699.83     202.11   3.463 0.000575 ***
## mnth4        1274.47     222.94   5.717 1.76e-08 ***
## mnth5        1446.49     255.26   5.667 2.32e-08 ***
## mnth6        1094.19     291.06   3.759 0.000188 ***
## mnth7         514.44     316.96   1.623 0.105139    
## mnth8         998.95     299.06   3.340 0.000892 ***
## mnth9        1660.57     265.43   6.256 7.77e-10 ***
## mnth10       1821.27     219.98   8.279 8.90e-16 ***
## mnth11       1257.98     202.41   6.215 9.93e-10 ***
## mnth12        965.67     188.31   5.128 4.02e-07 ***
## windspeed   -4647.50     509.95  -9.114  < 2e-16 ***
## hum         -3101.09     290.11 -10.689  < 2e-16 ***
## temp         5301.75     503.41  10.532  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 891.2 on 568 degrees of freedom
## Multiple R-squared:  0.7924, Adjusted R-squared:  0.7869 
## F-statistic: 144.6 on 15 and 568 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum + temp + workingday, 
##     data = traindata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4508.7  -376.2    98.8   557.5  2688.2 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2635.17     271.60   9.703  < 2e-16 ***
## yr           1998.53      75.18  26.582  < 2e-16 ***
## mnth2         120.61     189.30   0.637 0.524278    
## mnth3         702.96     201.50   3.489 0.000523 ***
## mnth4        1297.08     222.52   5.829 9.36e-09 ***
## mnth5        1469.05     254.71   5.768 1.32e-08 ***
## mnth6        1114.12     290.33   3.837 0.000138 ***
## mnth7         560.12     316.74   1.768 0.077535 .  
## mnth8        1019.87     298.32   3.419 0.000674 ***
## mnth9        1686.52     264.91   6.366 4.00e-10 ***
## mnth10       1839.15     219.47   8.380 4.19e-16 ***
## mnth11       1264.79     201.82   6.267 7.29e-10 ***
## mnth12        976.49     187.81   5.199 2.80e-07 ***
## windspeed   -4647.40     508.40  -9.141  < 2e-16 ***
## hum         -3120.22     289.37 -10.783  < 2e-16 ***
## temp         5220.01     503.37  10.370  < 2e-16 ***
## workingday    171.53      81.19   2.113 0.035065 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 888.5 on 567 degrees of freedom
## Multiple R-squared:  0.794,  Adjusted R-squared:  0.7882 
## F-statistic: 136.6 on 16 and 567 DF,  p-value: < 2.2e-16
## $Models
##   Formula                                                
## 1 "cnt ~ yr"                                             
## 2 "cnt ~ yr + mnth"                                      
## 3 "cnt ~ yr + mnth + windspeed"                          
## 4 "cnt ~ yr + mnth + windspeed + hum"                    
## 5 "cnt ~ yr + mnth + windspeed + hum + temp"             
## 6 "cnt ~ yr + mnth + windspeed + hum + temp + workingday"
## 
## $Fit.criteria
##   Rank Df.res   AIC  AICc   BIC R.squared Adj.R.sq    p.value Shapiro.W
## 1    2    582 10270 10270 10280    0.3268   0.3256  5.648e-52    0.9558
## 2   13    571  9814  9815  9876    0.7018   0.6955 2.705e-141    0.9263
## 3   14    570  9772  9773  9838    0.7235   0.7172 1.478e-149    0.9423
## 4   15    569  9711  9712  9781    0.7519   0.7458 8.691e-162    0.9474
## 5   16    568  9609  9610  9683    0.7924   0.7869 1.378e-182    0.9414
## 6   17    567  9606  9607  9685    0.7940   0.7882 1.852e-182    0.9433
##   Shapiro.p
## 1 3.099e-12
## 2 2.538e-16
## 3 2.748e-14
## 4 1.487e-13
## 5 2.061e-14
## 6 3.883e-14
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum + temp + workingday, 
##     data = traindata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4508.7  -376.2    98.8   557.5  2688.2 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2635.17     271.60   9.703  < 2e-16 ***
## yr           1998.53      75.18  26.582  < 2e-16 ***
## mnth2         120.61     189.30   0.637 0.524278    
## mnth3         702.96     201.50   3.489 0.000523 ***
## mnth4        1297.08     222.52   5.829 9.36e-09 ***
## mnth5        1469.05     254.71   5.768 1.32e-08 ***
## mnth6        1114.12     290.33   3.837 0.000138 ***
## mnth7         560.12     316.74   1.768 0.077535 .  
## mnth8        1019.87     298.32   3.419 0.000674 ***
## mnth9        1686.52     264.91   6.366 4.00e-10 ***
## mnth10       1839.15     219.47   8.380 4.19e-16 ***
## mnth11       1264.79     201.82   6.267 7.29e-10 ***
## mnth12        976.49     187.81   5.199 2.80e-07 ***
## windspeed   -4647.40     508.40  -9.141  < 2e-16 ***
## hum         -3120.22     289.37 -10.783  < 2e-16 ***
## temp         5220.01     503.37  10.370  < 2e-16 ***
## workingday    171.53      81.19   2.113 0.035065 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 888.5 on 567 degrees of freedom
## Multiple R-squared:  0.794,  Adjusted R-squared:  0.7882 
## F-statistic: 136.6 on 16 and 567 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr, data = testdata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4542.2 -1195.4   306.6  1285.1  3092.8 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   3342.4      183.3  18.234  < 2e-16 ***
## yr            2119.8      273.6   7.749 1.48e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1650 on 145 degrees of freedom
## Multiple R-squared:  0.2928, Adjusted R-squared:  0.2879 
## F-statistic: 60.04 on 1 and 145 DF,  p-value: 1.484e-12
## 
## Call:
## lm(formula = cnt ~ yr + mnth, data = testdata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3289.4  -394.7    20.8   475.4  2141.0 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1041.4      245.3   4.246 4.04e-05 ***
## yr            2131.0      164.5  12.951  < 2e-16 ***
## mnth2          617.0      365.8   1.687   0.0940 .  
## mnth3         1557.6      345.1   4.514 1.38e-05 ***
## mnth4         1914.7      342.3   5.593 1.21e-07 ***
## mnth5         3250.9      356.9   9.109 1.04e-15 ***
## mnth6         3843.8      351.7  10.928  < 2e-16 ***
## mnth7         3378.2      377.8   8.942 2.69e-15 ***
## mnth8         3363.0      357.9   9.397  < 2e-16 ***
## mnth9         4249.5      377.8  11.249  < 2e-16 ***
## mnth10        3566.3      389.9   9.146 8.47e-16 ***
## mnth11        2407.2      329.3   7.310 2.18e-11 ***
## mnth12         653.8      389.9   1.677   0.0959 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 945.3 on 134 degrees of freedom
## Multiple R-squared:  0.7854, Adjusted R-squared:  0.7662 
## F-statistic: 40.87 on 12 and 134 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed, data = testdata)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3034.09  -401.32    36.03   576.86  2208.72 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1320.3      302.2   4.368 2.50e-05 ***
## yr            2132.4      163.7  13.029  < 2e-16 ***
## mnth2          668.1      365.3   1.829   0.0697 .  
## mnth3         1704.9      355.9   4.790 4.39e-06 ***
## mnth4         2020.1      347.1   5.819 4.19e-08 ***
## mnth5         3263.9      355.1   9.192 6.86e-16 ***
## mnth6         3852.3      349.9  11.009  < 2e-16 ***
## mnth7         3382.8      375.8   9.002 2.01e-15 ***
## mnth8         3411.3      357.3   9.547  < 2e-16 ***
## mnth9         4260.8      375.8  11.337  < 2e-16 ***
## mnth10        3611.0      388.9   9.285 4.04e-16 ***
## mnth11        2451.8      328.8   7.457 1.02e-11 ***
## mnth12         631.4      388.1   1.627   0.1061    
## windspeed    -1684.3     1077.5  -1.563   0.1204    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 940.3 on 133 degrees of freedom
## Multiple R-squared:  0.7893, Adjusted R-squared:  0.7687 
## F-statistic: 38.32 on 13 and 133 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum, data = testdata)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2747.43  -443.93   -28.09   379.06  2473.29 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   3285.3      525.8   6.248 5.31e-09 ***
## yr            2088.0      153.6  13.594  < 2e-16 ***
## mnth2          302.9      351.9   0.861   0.3909    
## mnth3         1560.3      334.9   4.659 7.67e-06 ***
## mnth4         1960.7      325.3   6.027 1.57e-08 ***
## mnth5         3453.7      335.3  10.301  < 2e-16 ***
## mnth6         3510.3      336.6  10.428  < 2e-16 ***
## mnth7         3108.7      357.3   8.701 1.15e-14 ***
## mnth8         3336.9      335.0   9.960  < 2e-16 ***
## mnth9         4216.4      352.1  11.975  < 2e-16 ***
## mnth10        3541.2      364.5   9.714  < 2e-16 ***
## mnth11        2266.3      310.7   7.293 2.50e-11 ***
## mnth12         616.0      363.5   1.695   0.0925 .  
## windspeed    -2657.6     1032.7  -2.574   0.0112 *  
## hum          -2674.8      603.2  -4.434 1.93e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 880.5 on 132 degrees of freedom
## Multiple R-squared:  0.8166, Adjusted R-squared:  0.7972 
## F-statistic: 41.98 on 14 and 132 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum + temp, data = testdata)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2406.14  -298.26   -10.78   408.31  1780.92 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2200.48     526.87   4.177 5.37e-05 ***
## yr           1975.11     142.54  13.856  < 2e-16 ***
## mnth2          68.25     325.86   0.209  0.83443    
## mnth3         946.21     329.79   2.869  0.00480 ** 
## mnth4         886.52     365.08   2.428  0.01653 *  
## mnth5        1549.47     483.46   3.205  0.00170 ** 
## mnth6        1065.97     569.82   1.871  0.06362 .  
## mnth7         273.73     644.95   0.424  0.67195    
## mnth8         855.46     575.17   1.487  0.13934    
## mnth9        2344.44     488.65   4.798 4.30e-06 ***
## mnth10       2216.32     423.22   5.237 6.34e-07 ***
## mnth11       1707.78     305.19   5.596 1.23e-07 ***
## mnth12        276.70     339.81   0.814  0.41697    
## windspeed   -3304.90     955.23  -3.460  0.00073 ***
## hum         -2782.14     553.44  -5.027 1.60e-06 ***
## temp         5385.24    1055.33   5.103 1.15e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 807.3 on 131 degrees of freedom
## Multiple R-squared:  0.847,  Adjusted R-squared:  0.8295 
## F-statistic: 48.35 on 15 and 131 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum + temp + workingday, 
##     data = testdata)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2386.22  -327.65    -4.84   429.71  1842.87 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2027.67     540.11   3.754 0.000261 ***
## yr           1967.83     142.17  13.841  < 2e-16 ***
## mnth2          70.49     324.79   0.217 0.828514    
## mnth3         922.29     329.17   2.802 0.005858 ** 
## mnth4         866.86     364.15   2.380 0.018741 *  
## mnth5        1558.24     481.90   3.233 0.001550 ** 
## mnth6        1103.00     568.58   1.940 0.054555 .  
## mnth7         285.69     642.87   0.444 0.657495    
## mnth8         874.96     573.44   1.526 0.129490    
## mnth9        2398.06     488.61   4.908 2.71e-06 ***
## mnth10       2232.76     421.99   5.291 5.01e-07 ***
## mnth11       1721.46     304.35   5.656 9.39e-08 ***
## mnth12        265.20     338.79   0.783 0.435172    
## windspeed   -3194.17     955.50  -3.343 0.001083 ** 
## hum         -2696.31     555.16  -4.857 3.37e-06 ***
## temp         5341.36    1052.33   5.076 1.31e-06 ***
## workingday    190.33     139.13   1.368 0.173676    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 804.6 on 130 degrees of freedom
## Multiple R-squared:  0.8492, Adjusted R-squared:  0.8306 
## F-statistic: 45.75 on 16 and 130 DF,  p-value: < 2.2e-16
## $Models
##   Formula                                                
## 1 "cnt ~ yr"                                             
## 2 "cnt ~ yr + mnth"                                      
## 3 "cnt ~ yr + mnth + windspeed"                          
## 4 "cnt ~ yr + mnth + windspeed + hum"                    
## 5 "cnt ~ yr + mnth + windspeed + hum + temp"             
## 6 "cnt ~ yr + mnth + windspeed + hum + temp + workingday"
## 
## $Fit.criteria
##   Rank Df.res  AIC AICc  BIC R.squared Adj.R.sq   p.value Shapiro.W Shapiro.p
## 1    2    145 2599 2599 2608    0.2928   0.2879 1.484e-12    0.9650 8.402e-04
## 2   13    134 2446 2449 2488    0.7854   0.7662 7.023e-39    0.9510 4.773e-05
## 3   14    133 2445 2449 2490    0.7893   0.7687 1.409e-38    0.9593 2.470e-04
## 4   15    132 2427 2431 2475    0.8166   0.7972 1.142e-41    0.9633 5.857e-04
## 5   16    131 2402 2407 2453    0.8470   0.8295 6.647e-46    0.9493 3.463e-05
## 6   17    130 2402 2407 2456    0.8492   0.8306 1.896e-45    0.9545 9.362e-05
## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum + temp + workingday, 
##     data = testdata)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2386.22  -327.65    -4.84   429.71  1842.87 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2027.67     540.11   3.754 0.000261 ***
## yr           1967.83     142.17  13.841  < 2e-16 ***
## mnth2          70.49     324.79   0.217 0.828514    
## mnth3         922.29     329.17   2.802 0.005858 ** 
## mnth4         866.86     364.15   2.380 0.018741 *  
## mnth5        1558.24     481.90   3.233 0.001550 ** 
## mnth6        1103.00     568.58   1.940 0.054555 .  
## mnth7         285.69     642.87   0.444 0.657495    
## mnth8         874.96     573.44   1.526 0.129490    
## mnth9        2398.06     488.61   4.908 2.71e-06 ***
## mnth10       2232.76     421.99   5.291 5.01e-07 ***
## mnth11       1721.46     304.35   5.656 9.39e-08 ***
## mnth12        265.20     338.79   0.783 0.435172    
## windspeed   -3194.17     955.50  -3.343 0.001083 ** 
## hum         -2696.31     555.16  -4.857 3.37e-06 ***
## temp         5341.36    1052.33   5.076 1.31e-06 ***
## workingday    190.33     139.13   1.368 0.173676    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 804.6 on 130 degrees of freedom
## Multiple R-squared:  0.8492, Adjusted R-squared:  0.8306 
## F-statistic: 45.75 on 16 and 130 DF,  p-value: < 2.2e-16

6 Prediction

6.1 Prediction Model

## 
## Call:
## lm(formula = cnt ~ yr + mnth + windspeed + hum + temp + workingday, 
##     data = traindata)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4508.7  -376.2    98.8   557.5  2688.2 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2635.17     271.60   9.703  < 2e-16 ***
## yr           1998.53      75.18  26.582  < 2e-16 ***
## mnth2         120.61     189.30   0.637 0.524278    
## mnth3         702.96     201.50   3.489 0.000523 ***
## mnth4        1297.08     222.52   5.829 9.36e-09 ***
## mnth5        1469.05     254.71   5.768 1.32e-08 ***
## mnth6        1114.12     290.33   3.837 0.000138 ***
## mnth7         560.12     316.74   1.768 0.077535 .  
## mnth8        1019.87     298.32   3.419 0.000674 ***
## mnth9        1686.52     264.91   6.366 4.00e-10 ***
## mnth10       1839.15     219.47   8.380 4.19e-16 ***
## mnth11       1264.79     201.82   6.267 7.29e-10 ***
## mnth12        976.49     187.81   5.199 2.80e-07 ***
## windspeed   -4647.40     508.40  -9.141  < 2e-16 ***
## hum         -3120.22     289.37 -10.783  < 2e-16 ***
## temp         5220.01     503.37  10.370  < 2e-16 ***
## workingday    171.53      81.19   2.113 0.035065 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 888.5 on 567 degrees of freedom
## Multiple R-squared:  0.794,  Adjusted R-squared:  0.7882 
## F-statistic: 136.6 on 16 and 567 DF,  p-value: < 2.2e-16
## 
## Correlation of Coefficients:
##            (Intercept) yr    mnth2 mnth3 mnth4 mnth5 mnth6 mnth7 mnth8 mnth9
## yr         -0.19                                                            
## mnth2      -0.27        0.02                                                
## mnth3      -0.17        0.02  0.53                                          
## mnth4      -0.09        0.05  0.51  0.61                                    
## mnth5       0.00        0.07  0.49  0.62  0.68                              
## mnth6       0.00        0.08  0.45  0.61  0.69  0.77                        
## mnth7       0.01        0.12  0.44  0.60  0.69  0.78  0.82                  
## mnth8       0.02        0.09  0.45  0.61  0.69  0.78  0.81  0.83            
## mnth9       0.03        0.08  0.48  0.62  0.68  0.76  0.77  0.79  0.79      
## mnth10     -0.07        0.05  0.52  0.62  0.65  0.71  0.69  0.70  0.71  0.71
## mnth11     -0.20        0.04  0.52  0.57  0.57  0.59  0.56  0.56  0.57  0.59
## mnth12     -0.23        0.00  0.54  0.56  0.54  0.54  0.50  0.49  0.50  0.54
## windspeed  -0.54        0.04 -0.01  0.00 -0.05  0.03  0.04  0.07  0.06  0.06
## hum        -0.60        0.15  0.00  0.03  0.07  0.01  0.13  0.13  0.09 -0.03
## temp       -0.29       -0.14 -0.17 -0.40 -0.54 -0.68 -0.77 -0.82 -0.78 -0.70
## workingday -0.15        0.02  0.00  0.01  0.05  0.04  0.03  0.07  0.03  0.05
##            mnth10 mnth11 mnth12 windspeed hum   temp 
## yr                                                   
## mnth2                                                
## mnth3                                                
## mnth4                                                
## mnth5                                                
## mnth6                                                
## mnth7                                                
## mnth8                                                
## mnth9                                                
## mnth10                                               
## mnth11      0.60                                     
## mnth12      0.58   0.56                              
## windspeed   0.07   0.07   0.07                       
## hum        -0.06  -0.03  -0.10   0.19                
## temp       -0.53  -0.33  -0.22   0.02     -0.19      
## workingday  0.04   0.02   0.03   0.00     -0.03 -0.08
##                   2.5 %     97.5 %
## (Intercept)  2101.71462  3168.6343
## yr           1850.86068  2146.2033
## mnth2        -251.19573   492.4198
## mnth3         307.18582  1098.7429
## mnth4         860.01376  1734.1533
## mnth5         968.76147  1969.3405
## mnth6         543.86198  1684.3717
## mnth7         -62.01019  1182.2469
## mnth8         433.92378  1605.8081
## mnth9        1166.18822  2206.8434
## mnth10       1408.06850  2270.2287
## mnth11        868.38334  1661.1915
## mnth12        607.60203  1345.3819
## windspeed   -5645.98076 -3648.8185
## hum         -3688.58593 -2551.8488
## temp         4231.30386  6208.7085
## workingday     12.05783   330.9966